Reduced multitype critical branching processes in random environment

Abstract

Abstract We consider a multitype critical branching process Zn, n = 0, 1,…, in an i.i.d. random environment. Let Zm,n be the number of particles in this process at time m having descendants at time n. A limit theorem is proved for the logarithm of Znt,n at moments nt,0 ≤ t ≤ 1, conditioned on the survival of the process Zn up to moment n when n → ∞.